{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Sigmoid\n",
    "X1=np.linspace(-100,100,400)\n",
    "def sigmoid(x):\n",
    "    return 1/(1+np.exp(-x))\n",
    "y0 = sigmoid(X1)\n",
    "plt.plot(X1,y0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      0\n",
       "0   1.0\n",
       "1   1.0\n",
       "2   1.0\n",
       "3   1.0\n",
       "4   1.0\n",
       "..  ...\n",
       "95  1.0\n",
       "96  1.0\n",
       "97  1.0\n",
       "98  1.0\n",
       "99  1.0\n",
       "\n",
       "[100 rows x 1 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(np.ones(100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "df=pd.read_table('testSet.txt',header=None)\n",
    "df=pd.concat([df.iloc[:,:-1],pd.DataFrame(np.ones(100)),df.iloc[:,-1]],axis=1)\n",
    "df.columns = ['x0','x1','1','label']\n",
    "w = np.ones(3)\n",
    "alpha = 0.01"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = df.iloc[:,:-1]\n",
    "y = df.iloc[:,-1]\n",
    "y_hat = X.dot(w)\n",
    "\n",
    "grad = X.transpose().dot(y - y_hat)\n",
    "loop = 1000\n",
    "w = w + alpha * grad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "txt  = np.loadtxt('testSet.txt')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```\n",
    "梯度下降算法\n",
    "\n",
    "输入：\n",
    "    txt：读取 矩阵化数据\n",
    "    alpha：学习率\n",
    "    loops：迭代次数\n",
    "输出：\n",
    "    w：线性参数\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def BGD_LR(txt,alpha=0.01,loops=500):\n",
    "    #1.读取数据的维度\n",
    "    (m,n) = txt.shape\n",
    "\n",
    "    #2.扩充X增加【1】列\n",
    "    X = np.column_stack([txt[:,:-1],np.ones((m,1))])\n",
    "    #3.标签列\n",
    "    y =  txt[:,-1].reshape(m,1)\n",
    "    #4.线性参数\n",
    "    w = np.ones((X.shape[1],1))\n",
    "    ws = np.ones(X.shape[1])\n",
    "    #5.学习率\n",
    "    alpha = 0.01\n",
    "\n",
    "    #6.梯度下降法\n",
    "    for i in range(loops):\n",
    "        y_hat = sigmoid(X.dot(w))\n",
    "        w = w + alpha*X.T.dot(y - y_hat)/m\n",
    "    return w,ws\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "x0    -2.096282\n",
       "x1   -70.313582\n",
       "1     -6.076122\n",
       "dtype: float64"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "w1,ws1=BGD_LR(txt,0.01,5000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```\n",
    "w0 * x0 + w1 * x1 +w2 = 0\n",
    "x1 = (-w2 -w0 * x0)/w1\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plotBestFit(txt,w):\n",
    "    plt.scatter(txt[:,0],txt[:,1],c=txt[:,-1])\n",
    "    x2 = np.linspace(-3,3,60)\n",
    "    #决策边界，是 y = wx =0 的点\n",
    "    y2 = (-w[2]-w[0]*x2)/w[1]\n",
    "    plt.plot(x2,y2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "w,ws=BGD_LR(txt,0.01,5000)\n",
    "plotBestFit(txt,w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plotBestFit(txt, w1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(txt[:,0],txt[:,1],c=txt[:,-1])\n",
    "\n",
    "x2 = np.linspace(-4,4,80)\n",
    "y2 = w[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def SGD_LR(txt, alpha=0.01, loops=500):\n",
    "    # 1. 读取数据的维度\n",
    "    (m, n) = txt.shape\n",
    "    # 2. 扩充 X 增加 【1】 列\n",
    "    X = np.column_stack([txt[:,:-1], np.ones((m,1))])\n",
    "    # 3. 标签列\n",
    "    y = txt[:,-1].reshape(m,1)\n",
    "    \n",
    "    # 4. 线性参数\n",
    "    w = np.ones(X.shape[1])\n",
    "    \n",
    "    # ws = np.array(w)\n",
    "    # 5. 学习率\n",
    "    alpha = 0.01\n",
    "    \n",
    "    # 6. 梯度下降算法\n",
    "    for i in range(loops):\n",
    "        i = i % m\n",
    "        y_hat = sigmoid(X[i].dot(w))\n",
    "        w = w + alpha * X[i] * (y[i] - y_hat)\n",
    "        \n",
    "        # ws = np.append(ws, w, axis=0)\n",
    "    return w, ws"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def SGD_LR1(txt, alpha=0.01, loops=500):\n",
    "    # 1. 读取数据的维度\n",
    "    (m, n) = txt.shape\n",
    "    # 2. 扩充 X 增加 【1】 列\n",
    "    X = np.column_stack([txt[:,:-1], np.ones((m,1))])\n",
    "    # 3. 标签列\n",
    "    y = txt[:,-1].reshape(m,1)\n",
    "    \n",
    "    # 4. 线性参数\n",
    "    w = np.ones(X.shape[1])\n",
    "    \n",
    "    ws = np.array(w)\n",
    "    # 5. 学习率\n",
    "    alpha = 0.01\n",
    "   \n",
    "    # 6. 梯度下降算法\n",
    "    for i in range(loops):\n",
    "        indexs = (list(range(m)))\n",
    "        np.random.shuffle(indexs)\n",
    "        for j in range(m):\n",
    "            alpha = 4/(1 + j +i) + 0.01\n",
    "            y_hat = sigmoid(X[indexs[j]].dot(w))\n",
    "            w = w + alpha * X[indexs[j]] * (y[indexs[j]] - y_hat)\n",
    "            ws = np.append(ws, w, axis=0)\n",
    "    return w, ws"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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